Approval of the rules allows the House to consider the two bills on Thursday and Friday.
The votes came after two hours of debate in which Republicans said repeal would save billions of dollars, since the Congressional Budget Office has estimated that nearly all of the money going to the two programs would not be paid by the homeowner. Democrats argued that homeowners need these programs, even as Republicans pointed out that they have hardly been used so far.
Democrats also argued that Republicans want to repeal these programs even though they are not replacing them with anything else. Late in the debate, Rep. Jared Polis (D-Colo.) said Democrats would prefer to move ahead on a bill that prevents gas-price gouging by oil companies.
Several Democrats argued that Republicans have yet to bring up a "jobs bill," but Rep. Pete Sessions (R-Texas) rejected this, arguing that getting government out of the way and finding ways to reduce government debt are the best ways to create stability for workers.
-- This post was updated at 2:49 p.m.